with equality only for the Koebe function \(k(z)=z/(1-z)^2\) , or its rotation.
It is important to note that the Zalcman conjecture implies the celebrated Bieberbach conjecture \(|a_n|\le n\)  for \(f\in \mathcal {S}\) 
(see [1]}), and a well-known consequence of the area theorem shows that (REF ) holds for
\(n=2\)  (see [2]}). The Zalcman conjecture remains an open problem, even after de Branges' proof of the Bieberbach conjecture [3]}.
